Solve using elimination. 4x − 5y = –14 6x − 5y = 4 (_____, _____)

Write Equations: Write down the system of equations. 4x − 5y = –14 6x − 5y = 4Eliminate y: Since the coefficients of y are the same in both equations, we can eliminate y by subtracting the first equation from the second. (6x − 5y) − (4x − 5y) = 4 − (–14)Subtract Equations: Perform the subtraction to eliminate y. 6x − 5y − 4x + 5y = 4 + 14Simplify Equation: Simplify the equation. 2x = 18Solve for x: Solve for x by dividing both sides by 2. x = 18 / 2 x = 9Substitute x: Substitute x = 9 into one of the original equations to solve for y. We'll use the first equation. 4(9) − 5y = –14Perform Multiplication: Perform the multiplication. 36 − 5y = –14Isolate y Term: Subtract 36 from both sides to isolate the term with y. −5y = –14 − 36Simplify Right Side: Simplify the right side of the equation. −5y = –50Solve for y: Solve for y by dividing both sides by -5. y = –50 / -5 y = 10

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Solve using elimination. $\newline$ $4x - 5y = -14$ $\newline$ $6x - 5y = 4$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

4x - 5y = -14

\newline

6x - 5y = 4

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $4x − 5y = −14$ $\newline$ $6x − 5y = 4$
Eliminate y: Since the coefficients of y are the same in both equations, we can eliminate y by subtracting the first equation from the second. $\newline$ $(6x - 5y) - (4x - 5y) = 4 - (-14)$
Subtract Equations: Perform the subtraction to eliminate $y$ . $6x - 5y - 4x + 5y = 4 + 14$
Simplify Equation: Simplify the equation. $2x = 18$
Solve for x: Solve for x by dividing both sides by $2$ . $x = \frac{18}{2}$ $x = 9$
Substitute $x$ : Substitute $x = 9$ into one of the original equations to solve for $y$ . We'll use the first equation. $4(9) − 5y = –14$
Perform Multiplication: Perform the multiplication. $36 - 5y = -14$
Isolate y Term: Subtract $36$ from both sides to isolate the term with $y$ . $\newline$ $-5y = -14 - 36$
Simplify Right Side: Simplify the right side of the equation. $-5y = -50$
Solve for y: Solve for y by dividing both sides by -5＂).$\newline\$y = \frac{-50}{-5}$$\newline$$y = 10$